Staff Working Paper ERSD-2009-10
November 11, 2009
World Trade Organization
Economic Research and Statistics Division
This paper appears in the WTO working paper series in the context of the
WTO Academic Visiting Program
THE ECONOMICS OF TRADE AGREEMENTS IN THE LINEAR
COURNOT DELOCATION MODEL
Kyle Bagwell :
Stanford and NBER
Robert W. Staiger:
Stanford and NBER
Manuscript date:
October 8, 2009
Disclaimer: This is a working paper, and hence it represents research in progress. This
paper represents the opinions of the authors, and is the product of professional research. It is
not meant to represent the position or opinions of the WTO or its Members, nor the official
position of any staff members. Any errors are the fault of the authors. Copies of working
papers can be requested from the divisional secretariat by writing to: Economic Research and
Statistics Division, World Trade Organization, Rue de Lausanne 154, CH 1211 Geneva 21,
Switzerland. Please request papers by number and title.
The Economics of Trade Agreements in the Linear
Cournot Delocation Model
Kyle Bagwell
Stanford and NBER
Robert W. Staiger
Stanford and NBER
October 8, 2009
Abstract
Existing theories of trade agreements suggest that GATT/WTO e¤orts to reign in export
subsidies represent an ine¢ cient victory for exporting governments that comes at the expense
of importing governments. Building from the Cournot delocation model …rst introduced by
Venables (1985), we demonstrate that it is possible to develop a formal treatment of export
subsidies in trade agreements in which a more benign interpretation of e¤orts to restrain export
subsidies emerges. And we suggest that the gradual tightening of restraints on export subsidies
that has occurred in the GATT/WTO may be interpreted as deriving naturally from the gradual
reduction in import barriers that member countries have negotiated. Together with existing
theories, the Cournot delocation model may help to provide a more nuanced and complete
understanding of the treatment of export subsidies in trade agreements.
We thank Michele Ruta, Assaf Zimring and lecture participants at the WTO for very useful comments.
1
Introduction
The treatment of export subsidies in trade agreements is puzzling. It is often observed that export
subsidies distort market forces and lead to ine¢ cient patterns of trade, and that the use of export
subsidies should be restricted by international agreement for this reason. Formalizing this position,
however, has proven to be surprisingly elusive. In fact, formal arguments for the treatment of export
subsidies in trade agreements point to a starkly di¤erent conclusion: rather than restrain export
subsidies, international agreements should, if anything, encourage them.1 At a basic level, this
conclusion re‡ects the trade-volume-expanding nature of export subsidies, which generally aligns
these policies with the purpose of a trade agreement.
In practice, the treatment of export subsidies is also complex, and has evolved over time from
the early years of the General Agreement on Tari¤s and Trade (GATT) to the creation of GATT’s
successor, the World Trade Organization (WTO).2 In the early GATT era, a permissive stance was
taken on export subsidies, amounting to little more than reporting requirements. Over time GATT
restrictions on the use of export subsidies were progressively tightened, and during the …nal GATT
negotiation round (the Uruguay Round) in which the WTO was created, a more comprehensive
approach to subsidies was introduced in the Agreement on Subsidies and Countervailing Measures
(the SCM Agreement) which includes a prohibition on the use of export subsidies.3
Theoretical attempts to understand and interpret the treatment of export subsidies in trade
agreements face two challenges. A …rst challenge is to …nd situations in which a government actually
would be tempted to use an export subsidy. A second challenge is to show that a ceiling on export
subsidies would then be bene…cial for the negotiating governments. The …rst step has been taken
in the distinct literatures on strategic trade policy and on the political economy of trade policy.
The second step is especially perplexing. To be sure, for the models developed in these literatures,
the governments of exporting countries could enjoy mutual gains from an agreement to impose
ceilings on export subsidies. But once importing-country welfare is considered, mutual gains for
the negotiating governments would require that exporting countries face ‡oors on export subsidies.4
Therefore, the existing theories imply a provocative interpretation of GATT/WTO e¤orts to reign
in export subsidies: these e¤orts represent an ine¢ cient victory for exporting governments that
comes at the expense of importing governments.
In this paper, we demonstrate that it is possible to develop a formal treatment of export
subsidies in trade agreements in which a more benign interpretation of the GATT/WTO e¤orts
to reign in export subsidies emerges. And we suggest that the gradual tightening of restraints on
export subsidies that has occurred in the GATT/WTO may be interpreted as deriving naturally
from the gradual reduction in import barriers that member countries have negotiated. To make
1
See, for example, the discussion in Bagwell and Staiger (2002, Ch. 10).
See Sykes (2005) on the evolution of subsidy rules in the GATT/WTO.
3
The WTO’s Agreement on Agriculture provides further elaboration of the rules on subsidies as they apply to
agricultural goods.
4
This is true in the seminal strategic export subsidy model of Brander and Spencer (1985), and it is also true
when export subsidies re‡ect political economy motives (see Bagwell and Staiger, 2001).
2
1
these points, we adopt the Cournot delocation model …rst introduced by Venables (1985). Venables
shows that, if countries start at global free trade (i.e., at a set of policies such that each country
sets its import and export policy at free trade), then a country gains by introducing a small export
subsidy and its trading partner loses. Assuming that countries start at global free trade, Venables
also shows that a country gains, and its trading partner again loses, when the country imposes
a small import tari¤. Venables does not characterize the Nash equilibrium in import and export
policies, though, and so does not address the …rst step mentioned above, namely, con…rming that a
government actually would use an export subsidy. As well, he does not consider e¢ ciency, and so
does not assess the second step mentioned above, namely, con…rming that negotiated restraints on
export subsidies could lead to mutual gains for the negotiating governments. We focus on a linear
model and address both steps.
More speci…cally, we consider trade policies and agreements in the linear Cournot delocation
model. In this model, two countries trade a given homogeneous good subject to trade costs. The
markets are segmented and …rms compete as Cournot competitors, leading to the possibility of
two-way trade in identical products. This model exhibits a …rm-delocation e¤ect, whereby a higher
trade cost along one channel of trade increases the number of …rms in the importing country and
decreases the number of …rms in the exporting country. And as Venables (1985) emphasizes, by
altering the intensity of Cournot competition across markets, the …rm-delocation e¤ect can give
rise to novel reasons for unilateral trade policy intervention.
We …rst o¤er a thorough analysis of the manner in which prices and trade volumes respond to
changes in trade costs such as a change in an import or export tax. Following Venables (1985), we
then show that, starting at global free trade, the introduction of a small import tari¤ or export
subsidy generates a welfare gain for the intervening country and a welfare loss for its trading partner.
We also establish that an e¢ cient set of trade policies in this model entails a net trade tax of zero
along each channel of trade; for example, countries achieve an e¢ cient outcome under global free
trade. Viewed together, these …ndings suggest a potential e¢ ciency-enhancing interpretation for
WTO rules, which place ceilings on import tari¤s and export subsidies.
We show, however, that this interpretation is subtle. In particular, we also consider the Nash
equilibrium in trade policies, and we …nd that export taxes are used in the Nash equilibrium, in
addition to import tari¤s. Thus, if the trade policies of countries are su¢ ciently close to their
non-cooperative levels, then a ceiling on export subsidies by itself would be meaningless.
The …nding that countries employ export taxes under non-cooperative interaction arises as well
in traditional models that feature perfectly competitive markets; however, it is perhaps unexpected
in the Cournot delocation model, given that the optimal export-policy departure from global free
trade involves the introduction of an export subsidy. To interpret our characterization of the Nash
equilibrium, we show that, if a country’s trade policies start at free trade, then that country could
gain by introducing a small import tari¤ combined with a small export tax, where these policy
changes are set so as to maintain the free-trade price in the intervening country. This unilateral
variation leaves unaltered the level of consumer surplus in the intervening country while generating
2
greater tari¤ revenue for this country. We provide further interpretation of the Nash equilibrium
by showing that, if a country’s trade policies start in the neighborhood of free trade, then a
novel tari¤-complementarity e¤ect exists, whereby the country’s import and export tari¤s exert a
complementary e¤ect on its tari¤ revenue.
With these results in place, we may then understand why a country is unlikely to use an export
subsidy when it is already imposing a signi…cant import tari¤. Intuitively, an import tari¤ induces
entry by …rms in the intervening country via the …rm-delocation e¤ect, which ultimately increases
exports and raises the cost of an export-subsidy program. Moreover, we may also understand
why, in the presence of a signi…cant import tari¤, an export tax begins to look appealing: by
inducing entry of …rms in the intervening country’s trading partner, the …rm-delocation e¤ect that
is associated with the export tax raises the volume of imports on which the import tari¤ is applied,
thereby enhancing the revenue bene…ts of the import tari¤.
In the Nash equilibrium, therefore, an export tax is used in conjunction with an import tari¤.
If a tight ceiling on import tari¤s is imposed, however, then a country may be tempted to use an
export subsidy. From this perspective, we may speculate that the imposition over time in the WTO
of tighter restrictions on the use of export subsidies may ultimately be explained by the success
that this institution has had over time in facilitating negotiations leading to tighter ceilings on
import tari¤s by member countries. We thus provide a subtle and potentially rich interpretation
of the treatment of export subsidies in the WTO.
Finally, we return to a theme raised in a companion paper (Bagwell and Staiger, 2009) and
consider the “politically optimal” policies (the unilateral trade policies that would be chosen if
governments were not motivated by the terms-of-trade implications of their respective trade policy
selections) in the linear Cournot delocation model. We …nd that a unique symmetric political
optimum exists and that it entails global free trade. Thus, if governments were not motivated
by the terms-of-trade implications of their trade policies, then they would achieve an e¢ cient
outcome, and in particular each government would eliminate all tari¤s and subsidies on imports as
well as exports. The prohibition of export subsidies contained in the WTO SCM Agreement is thus
compatible with the political optimum in this model. This feature further strengthens the ability
of the linear Cournot delocation model to provide an interpretation of the treatment of export
subsidies in the GATT/WTO, given that other design features of the GATT/WTO can also be
interpreted as guiding governments toward e¢ cient politically optimal outcomes (see Bagwell and
Staiger, 1999a, 2009).
The remainder of the paper is organized as follows. In section 2 we develop the linear Cournot
delocation model. Section 3 then characterizes unilateral and e¢ cient trade policies, establishing
that global free trade is e¢ cient and that from this starting point each country would desire the
introduction of a small import tari¤ or export subsidy. Section 4 derives the Nash equilibrium trade
policies, and establishes that the Nash policies involve import tari¤s and export taxes. In section
5 we o¤er an interpretation of these trade policy …ndings. Finally, section 6 establishes that the
unique symmetric politically optimal policies entail global free trade, while section 7 concludes.
3
2
Cournot Delocation Model
In this section, we develop our model. The model entails two countries that trade a given homogeneous good, where the markets are segmented and …rms compete as Cournot competitors. We
begin by analyzing the model in a “short-run”setting in which the number of …rms is …xed in each
country. We then allow for endogenous entry and exit and thus adopt a “long-run” orientation.
We present short- and long-run comparative statics results. In later sections, we use this model to
analyze trade policies.
2.1
Basic Assumptions
We focus on a good that is produced and consumed in both a domestic or home country and in
a foreign country, and we use asterisks ( ) to denote foreign-country variables.5 The respective
markets are segmented, and so prices may di¤er across the two markets. The …rms compete in a
Cournot fashion. As is well known, in this setting, two-way (intra-industry) trade may occur.
To keep the analysis tractable, we assume that demand and cost functions are linear. With the
domestic price denoted as P and the foreign price denoted as P , the inverse domestic and foreign
demand functions are then given by P (Q) = 1
Q and P (Q ) = 1
Q , respectively, where Q
denotes the units of the good supplied to the domestic market and Q denotes the units of the
good supplied to the foreign market. Whether a …rm is located in the domestic or foreign market,
the …rm has a constant marginal cost of production, c, where 1 > c
0. Each …rm also incurs a
…xed cost F > 0 upon entry. We assume that the …xed cost is never so large as to preclude entry
by more than one …rm.
Finally, when a domestic …rm exports output to the foreign market, it incurs a per-unit trade
cost of
> 0; likewise, when a foreign …rm exports output to the domestic market, it incurs a
per-unit trade cost of
> 0. As discussed further in the next section, the trade cost facing any
…rm is the sum of the speci…c export tari¤ that its own country imposes, the speci…c import tari¤
that the other country imposes, and the per-unit transport cost,
> 0. Throughout we assume
that these trade costs are non-prohibitive.
2.2
Short-Run Analysis
We …rst present our short-run analysis, where the number of …rms in each country is taken as …xed.
Let nh be the number of home …rms and nf be the number of foreign …rms.
We begin by considering the output choices of some home …rm i. Let qhi be the output for home
…rm i that is sold in the home market, qh be the output of each other home …rm for sales in the
home market, and qf be the output of each foreign …rm for sales in the home market. Similarly,
let qhi be the output for home …rm i that is sold in the foreign market, qh be the output of each
other home …rm for sales in the foreign market, and qf be the output of each foreign …rm for sales
5
As usual, the model can be interpreted in general-equilibrium terms with the addition of a freely traded second
good that enters quasi-linearly into utility.
4
in the foreign market. With these de…nitions in place, we may de…ne the short-run pro…t function
for home …rm i as
hi
= [P (qhi + (nh
+[P (qhi + (nh
Recall that
c]qhi
1)qh + nf qf )
1)qh + nf qf )
(1)
)]qhi
(c +
F:
> 0 denotes the total trade cost expressed in speci…c (per unit) terms for sales of
domestic …rms in the foreign market.
A domestic …rm chooses qhi and qhi to maximize its short-run pro…t. Using (1), the …rst-order
conditions for pro…t maximization are given by
P (qhi + (nh
P (qhi + (nh
c = qhi
1)qh + nf qf )
1)qh + nf qf )
(2)
) = qhi ;
(c +
from which the short-run reaction functions for home …rm i may be derived:
qhi (qh ; qf ; nh ; nf ) =
qhi (qh ; qf ; nh ; nf ;
) =
1
(nh
1
(nh
1)qh
2
1)qh
nf q f
c
nf q f
(c +
2
)
:
We may now impose within-country symmetry and set qh = qhi and qh = qhi . This yields the
home-…rm reaction functions:
1
nf q f c
nh + 1
1 nf qf (c +
qh (qf ; nh ; nf ) =
qh (qf ; nh ; nf ;
) =
(3)
)
nh + 1
:
As expected, the reaction function for home …rms in the domestic market is decreasing in the
number of units imported from abroad, nf qf , the number of domestic …rms, nh , and the marginal
cost of production associated with domestic sales, c. Similarly, the reaction function for home
…rms in the foreign market is decreasing in the number of units sold by foreign …rms in the foreign
market, nf qf , the number of domestic …rms, nh , and the marginal cost of foreign sales, c +
.
Consider next the output choices of some foreign …rm i. Let qfi denote the output of foreign
…rm i for sales in the foreign market and qfi denote the output for foreign …rm i for sales in the
foreign market. The short-run pro…t function for foreign …rm i is then de…ned as
fi
= [P (qfi + (nf
+[P (qfi
where recall that
(nf
1)qf + nh qh )
1)qf
nh q h )
c]qfi
(c + )]qfi
(4)
F;
> 0 denotes the total trade cost expressed in speci…c (per unit) terms for sales
of foreign …rms in the domestic market. With the …rst-order conditions for pro…t maximization
5
given by
P (qfi + (nf
P (qfi
(nf
c = qfi
1)qf + nh qh )
1)qf
nh q h )
(c + ) =
(5)
qfi ;
we proceed exactly as above to derive the short-run reaction functions for foreign …rm i, and then
impose within-country symmetry by setting qf = qfi and qf = qfi to arrive at the foreign-…rm
reaction functions:
1
nh q h c
nf + 1
1 nh qh (c + )
nf + 1
qf (qh ; nh ; nf ) =
qf (qh ; nh ; nf ; ) =
(6)
As (6) reveals, the short-run comparative statics for a foreign …rm also take the expected signs.
Using (3) and (6), we may now solve for the Cournot-Nash equilibrium quantities in each of the
two (segmented) markets. For the home market, we …nd
qhN (nh ; nf ; ) =
qfN (nh ; nf ; ) =
1 c + nf
1 + nh + nf
1 c
(1 + nh )
:
1 + nh + nf
(7)
As expected, each home …rm produces more in the domestic market when its marginal cost of
production is lower, the trade cost facing foreign …rms is higher, and the number of domestic or
foreign …rms is lower. Likewise, each foreign …rm produces more in the domestic market when
its marginal cost of production is lower, the trade cost that it faces is lower, and the number of
domestic or foreign …rms is lower. Letting the aggregate Cournot-Nash quantity in the home market
be expressed as QN
nh qhN + nf qfN , it then follows from (7) that
QN (nh ; nf ; ) =
(nh + nf )(1 c)
1 + nh + nf
P N (nh ; nf ; )
1
QN (nh ; nf ; ) =
nf
(8)
1 + cnh + (c + )nf
:
1 + nh + nf
The Cournot output (price) in the domestic market decreases (increases) with the trade cost, ,
and increases (decreases) with the numbers of domestic and foreign …rms, nh and nf .
Likewise, for the foreign market, we …nd
qf N (nh ; nf ;
) =
qhN (nh ; nf ;
) =
1 c + nh
1 + nh + nf
1 c
(1 + nf )
:
1 + nh + nf
6
(9)
Letting the aggregate Cournot-Nash quantity in the foreign market be expressed as Q
N
nh qhN +
nf qf N , we have from (9) that
Q
N
(nh ; nf ;
) =
(nh + nf )(1 c)
1 + nh + nf
P
N
(nh ; nf ;
)
1
Q
N
(nh ; nf ;
nh
)=
(10)
1 + cnf + (c + )nh
:
1 + nh + nf
Thus, the Cournot output (price) in the foreign market decreases (increases) with the trade cost,
, and increases (decreases) with the numbers of domestic and foreign …rms, nh and nf .
Finally, the Cournot-Nash quantities from (7) and (9) may be plugged into the domestic-…rm
pro…t expression found in (1) to de…ne the short-run maximized pro…t of a home …rm:
h
(nh ; nf ;
[P N (nh ; nf ; )
; )
+[P
N
(nh ; nf ;
c]qhN (nh ; nf ; )
)
(c +
)]qhN (nh ; nf ;
)
F:
Using the …rst-order condition for pro…t maximization as represented in (2), we may simplify and
write
h
; ) = (qhN (nh ; nf ; ))2 + (qhN (nh ; nf ;
(nh ; nf ;
))2
F:
Similarly, using (7), (9) and (4), we …nd that the short-run maximized pro…t of a foreign …rm is
f
(nh ; nf ;
; )
[P
N
(nh ; nf ;
)
+[P N (nh ; nf ; )
c]qf N (nh ; nf ;
)
(c + )]qfN (nh ; nf ; )
F:
Using the …rst-order conditions for pro…t maximization as found in (5), we may again simplify and
write
f
; ) = (qf N (nh ; nf ;
(nh ; nf ;
))2 + (qfN (nh ; nf ; ))2
F:
We complete our short-run analysis of the model by considering comparative statics properties
for the maximized pro…t functions. These properties are essential below, when we analyze the
long-run implications of changes in trade policies. For a home …rm, we …nd that
@
h (n
h ; nf ;
; )
@
@ h (nh ; nf ;
@
; )
@qhN
>0
@
@q N
= 2qhN h < 0;
@
= 2qhN
(11)
where for notational simplicity we suppress functional dependencies on the right-hand side of these
expressions. Thus, an increase in the trade cost
that confronts foreign exporters generates an
increase in pro…t for a home …rm, whereas an increase in the trade cost
that a home …rm faces
when exporting results in a decrease in pro…t for a home …rm. Turning now to the e¤ect on a home
7
…rm’s pro…t of changes in the numbers of …rms, we …nd
@
h (n
h ; nf ;
; )
@nh
h
@ (nh ; nf ;
@nf
; )
@qhN
@q N
+ 2qhN h < 0
@nh
@nh
N
@q
@q N
= 2qhN h + 2qhN h < 0:
@nf
@nf
= 2qhN
(12)
Thus, home …rm pro…t also falls when there is an increase in the number of domestic or foreign
…rms.
Similarly, for a foreign …rm, we …nd that
@
f (n
h ; nf ;
; )
@
f
@ (nh ; nf ;
@
; )
= 2qfN
@qfN
<0
@
@qf N
= 2qf N
> 0;
@
(13)
and
@
f (n
h ; nf ;
; )
@nf
@
f (n
h ; nf ;
; )
@nh
= 2qf N
= 2qf N
@qf N
@nf
@qf N
@nh
+ 2qfN
+ 2qfN
@qfN
@nf
@qfN
@nh
<0
(14)
< 0:
These …ndings may be interpreted in an analogous fashion.
2.3
Long-Run Analysis and the Firm-Delocation E¤ect
Thus far we have assumed that the numbers of domestic and foreign …rms are …xed. A shortrun modeling framework is appropriate for understanding how trade policies may shift pro…ts
between domestic and foreign …rms, and indeed much of the strategic-trade literature employs this
framework. In this paper, however, we are interested in the long-run e¤ects of trade policy. We are
therefore led to consider the manner in which trade policies may change the numbers of domestic
and foreign …rms as well as the outputs of individual …rms. To this end, we now shift our focus to
the long run and use the short-run analysis above as a means of de…ning and analyzing the long-run
industry equilibrium.
The key feature of the long-run analysis is that the numbers of domestic and foreign …rms are
endogenously determined by free-entry conditions. We thus now de…ne the free-entry numbers of
N
…rms, nN
h ( ; ) and nf ( ; ), as the solutions to the free-entry conditions:
h
(nh ; nf ;
; )=0=
f
(nh ; nf ;
; ):
(15)
In all of our subsequent analysis, we assume that the numbers of domestic and foreign …rms adjust
to ensure that the free-entry conditions captured in (15) are satis…ed.
N
We can analyze nN
h ( ; ) and nf ( ; ) as the solutions to the 2x2 system presented by (15).
8
This system has the following Jacobian determinant:
@ f@ h
@ h@ f
@nh @nf
@nh @nf
2
= (
)2 [qhN qf N
1 + nh + nf
(16)
jJj =
qhN qfN ]2 > 0;
where the …nal expression is derived using (12) and (14). The inequality in (16) is important and
follows since
under our assumption that
qhN
qhN
=
qf N
qfN
=
+ nf ( + )
> 0, and
1 + nh + nf
+ nh ( + )
>0
1 + nh + nf
> 0 and
(17)
> 0. The inequalities featured in (17) capture a local-
market bias in …rm sales: each …rm produces more for sales in its local market than for export,
when trade costs are positive. Given that the …rms are otherwise symmetric, this means as well
that each …rm sells more in its local market than do …rms that export into this market:
qhN
qf N
qfN
=
qhN
=
> 0, and
> 0:
As will become clear below, the local-market bias in …rm sales plays a critical role in determining
the long-run implications of trade policies.
We next conduct long-run comparative statics on the numbers of domestic and foreign …rms.
Using the signs for partial derivatives of maximized pro…t functions as derived above in (11)-(14),
along with the sign of the Jacobian as given in (16), it is direct to con…rm that nN
h ( ; ) is
decreasing in
in
and increasing in
and similarly that nN
f ( ; ) is increasing in
and decreasing
. Thus, we observe the presence of a …rm-delocation e¤ ect: a higher trade cost along one
channel increases the number of …rms in the importing country and decreases the number of …rms
in the exporting country.
For future use, we require explicit expressions for the …rm-delocation e¤ects associated with
changes in trade policies. In particular, we …nd that a change in the trade cost that a¤ects foreign
exports induces the following changes in the numbers of domestic and foreign …rms:
@nN
h
@
@nN
f
@
=
=
N 2
N 2
N
N
N N
N N
[qhN nN
f ((qf ) + (qf ) ) + qf (1 + nh )(qh qf + qh qf )]
[qhN qf N
qhN qfN ]2
>0
N 2
N 2
N N N N
N N
[qfN (1 + nN
h )((qh ) + (qh ) ) + qh nf (qh qf + qh qf )]
[qhN qf N
qhN qfN ]2
(18)
<0
where our expressions suppress notational dependencies. Similarly, a change in the trade cost that
a¤ects domestic exports results in the following changes in the numbers of domestic and foreign
9
…rms:
@nN
h
@
@nN
f
@
=
=
N 2
N 2
N N N N
N N
[qhN (1 + nN
f )((qf ) + (qf ) ) + qf nh (qh qf + qh qf )]
[qhN qf N
qhN qfN ]2
N 2
N 2
N
N
N N
N N
[qf N nN
h ((qh ) + (qh ) ) + qh (1 + nf )(qh qf + qh qf )]
[qhN qf N
qhN qfN ]2
<0
(19)
> 0:
Thus, as previously indicated, an increase in the trade cost along any one channel of trade causes
a decrease in the number of …rms in the exporting country and an increase in the number of …rms
in the importing country.
Finally, we de…ne the following long-run price and quantity functions. It is apparent that the
long-run prices are ultimately functions of the trade costs:
PeN ( ; )
Pe
N
( ; )
N
P (QN (nN
h ( ; ); nf ( ; ); ))
P (Q
N
N
(nN
h ( ; ); nf ( ; );
)):
Similarly, the long-run outputs of domestic and foreign …rms in the domestic market is ultimately
determined by the underlying trade costs:
qehN ( ; )
qefN ( ; )
N
qhN (nN
h ( ; ); nf ( ; ); )
N
qfN (nN
h ( ; ); nf ( ; ); ):
Of course, the long-run outputs of domestic and foreign …rms in the foreign market may be similarly
characterized:
qehN ( ; )
N
qef ( ; )
N
qhN (nN
h ( ; ); nf ( ; );
qf
N
(nN
h (
;
); nN
f (
; );
)
):
These de…nitions identify the precise channels through which trade costs alter long-run prices and
quantities. Our next step is to characterize the overall e¤ect that a change in a trade cost has on
long-run prices and trade volumes.
2.4
Long-Run Comparative Statics on Prices
The comparative statics results for prices re‡ect the …rm-delocation e¤ect. In particular, observe
that
N
@ PeN ( ; )
@QN @nN
@QN @nf
@QN
h
= P 0 (QN )[
+
+
]:
@
@nh @
@nf @
@
Using (8) and (18), we …nd that
qefN qehN
@ PeN ( ; )
= N N
< 0;
@
[e
qh qef
qehN qefN ]
10
(20)
where the inequality uses the fact that (16) holds in particular at the free-entry values for the
numbers of domestic and foreign …rms under our assumption that
> 0 and
> 0. In other
words, we see from (20) that long-run prices in this model behave in a surprising manner and in
fact exhibit the Metzler paradox: a higher import tari¤ (or a higher foreign export tari¤) induces
so much domestic entry that the local domestic price actually falls.
Next, consider the e¤ect on PeN of an increase in . We have
N
N
N
@ PeN ( ; )
@QN @nf
0
N @Q @nh
= P (Q )[
+
]:
@
@nh @
@nf @
Using (8), (19) and (16), it follows that
under our assumption that
qef N qehN
@ PeN ( ; )
>0
= N N
@
[e
qh qef
qehN qefN ]
> 0 and
(21)
> 0. Thus, according to (21), when domestic …rms incur
a higher trade cost as exporters, exit in the domestic country occurs to such a degree that the
domestic price actually rises.
Of course, exactly analogous results hold for the price in the foreign country. In particular,
employing (10), (18), (19), (16) and our assumption that
> 0 and
> 0; and proceeding as
above, we …nd that
and
@ Pe
N(
@ Pe
N(
; )
@
@
; )
=
=
qefN qehN
< 0:
(22)
qehN qefN
> 0:
(23)
[e
qhN qef N
qehN qefN ]
[e
qhN qef N
qehN qefN ]
The price e¤ects of trade taxes described by (20) through (23) represent the most striking
implication of the …rm-delocation e¤ect, but they are not by themselves enough to determine the
impact of trade taxes on welfare. In order to determine that, we need to know as well how trade
taxes impact trade volumes. We turn to this question next.
2.5
Long-Run Comparative Statics on Trade Volumes
Trade taxes impact trade volumes in this model through two channels: they e¤ect the export sales
per …rm in a given country; and they e¤ect the number of …rms located in that country. We have
already derived expressions for the second channel. What remains is to derive expressions for the
…rst channel, so that we may then evaluate the impact of trade taxes on trade volumes.
Notice that, for a given market and any given numbers of domestic and foreign …rms, and using
the linear structure of our model, the …rst-order conditions (2) and (5) for pro…t maximization
imply that a …rm’s best-response and thus Cournot-Nash quantity must equal the e¤ective markup
for the …rm in that market. Consequently, we may use our knowledge of how long-run prices vary
11
with trade costs, as captured above in equations (20)-(23), to deduce how long-run …rm quantities
vary with trade costs.
Consider, then, export sales per home …rm qehN ( ; ) .We know from (2) that, for given trade
costs and numbers of …rms, P (QN )
(c + ) = qhN . This relationship must hold in particular at
the free-entry numbers of …rms; thus, Pe N ( ; ) (c + ) = qehN ( ; ). Using (23) and (22), we
may therefore conclude that
@ qehN ( ; )
@
@ Pe
=
@ qehN ( ; )
@
@ Pe
=
N(
; )
@
N(
=
; )
@
qehN qefN
>0
[e
qhN qef N
qehN qefN ]
[e
qhN qef N
1=
qehN qefN ]
qehN qef N
(24)
< 0:
Thus, when the trade cost imposed on foreign exports rises, domestic entry and foreign exit occur.
The foreign exit is su¢ ciently intense that the foreign price actually rises, with the result that
each domestic …rm now exports more. Likewise, when the trade cost imposed on domestic exports
rises, foreign entry is unleashed to such an extent that the price in the foreign market falls. With
domestic …rms now receiving a lower e¤ective markup on exports, both because of the higher trade
cost and the lower foreign market price, domestic …rms export less.
Of course, similar …ndings obtain for the export sales per foreign …rm qefN ( ; ). For given
trade costs and numbers of …rms, we know from (5) that P (QN ) (c + ) = qfN . Evaluating at
the free-entry numbers of …rms, we thus have that PeN ( ; ) (c + ) = qefN ( ; ). Using (20) and
(21), we may therefore conclude that
@ qefN ( ; )
@
@ qefN ( ; )
@
=
=
@ PeN ( ; )
@
1=
qehN qef N
[e
qhN qef N
<0
qehN qefN ]
(25)
qef N qehN
@ PeN ( ; )
> 0:
= N N
@
qehN qefN ]
[e
qh qef
Thus, when the trade cost imposed on foreign exports is increased, domestic entry occurs and the
domestic price falls. Due to the reduced domestic price as well as the direct cost of the higher trade
cost, each foreign …rm reduces its exports to the domestic market. When the trade cost imposed
on domestic exports is increased, domestic exit occurs, the domestic price rises, and so each foreign
…rm exports more to the domestic market.6
6
We emphasize the impacts of trade costs on export volumes because these impacts will enter directly in the
analysis below. But the impacts of trade costs on local-market sales volumes predicted by the model may be of some
independent interest, because they are somewhat surprising. Speci…cally, proceeding as above, it is direct to establish
that an increase in the trade cost imposed on foreign exports leads each domestic …rm to reduce its local-market sales
and leads each foreign …rm to increase its local-market sales; in particular, we …nd that
0 and
@ qef N (
@
; )
=
N N
qeh
qef
Nq
[e
qh
ef N
N]
qehN qef
N
@ qeh
(
@
; )
=
N
qef
qehN
Nq
[e
qh
ef N
N]
qehN qef
<
> 0. And similarly, an increase in the trade cost imposed on domestic exports
leads each domestic …rm to increase its local-market sales and leads each foreign …rm to reduce its local-market sales;
in particular, we …nd that
N
@ qeh
(
@
; )
=
qef N qehN
Nq
[e
qh
ef N
N]
qehN qef
> 0 and
12
@ qef N (
@
; )
=
N
qef
qehN
Nq
[e
qh
ef N
N]
qehN qef
< 0.
Armed with (24) and (25) as well as our earlier expressions (18) and (19), we may now turn
to the …nal task of this section and consider how long-run trade volumes vary with trade costs.
As noted above, an understanding of the relationship between export volumes and trade costs is
needed to determine the impact of trade taxes on welfare, which is in turn important for subsequent
sections, when we consider the determination of unilateral, e¢ cient and Nash trade policies. We
present our …ndings initially without an assumption that symmetric trade policies are adopted for
the domestic and foreign markets. We then assume symmetric trade policies and report simpli…ed
expressions.
To begin, we de…ne the home country’s export volume as
EN ( ; )
nN
qhN ( ; ):
h ( ; )e
(26)
Now consider how the domestic export volume varies with the trade cost that confronts foreign
exports. Using (26), we have that
@ qehN ( ; )
@nN ( ; )
@E N ( ; )
= nN
+ qehN ( ; ) h
> 0;
h ( ; )
@
@
@
where the inequality follows from (24) and (18). Thus, if foreign exporters confront a higher trade
cost, then the number of domestic …rms, the export sales of each domestic …rm and thus the volume
of domestic exports must rise. Using (24) and (18), we may derive the following expression:
=
@E N ( ; )
@
N q N )2 + (e
Nq
qfN )2 ] + qehN qefN (e
qf N )2 + (e
ehN qehN [(e
qhN )2 ] + nN
q
e
nN
qhN qefN + qehN qef N )
f q
h
h f ef [(e
[e
qhN qef N
qehN qefN ]2
(27)
> 0:
Next, consider how the domestic export volume varies with the trade cost that confronts domestic exports. Referring to (26), we see that
@ qehN ( ; )
@nN ( ; )
@E N ( ; )
= nN
+ qehN ( ; ) h
< 0;
h ( ; )
@
@
@
where the inequality follows from (24) and (19). Thus, if the trade cost that faces domestic exporters
increases, then the number of domestic …rms, the export volume of each domestic …rm and thus
the volume of domestic exports must fall. Referring to (24) and (19), we may derive the following
useful expression:
@E N ( ; )
=
@
nN
qf N )2 ((e
qhN )2 + (e
qhN )2 ) + (e
qhN )2 (1 + nN
qf N )2 + (e
qfN )2 )
h (e
f )((e
[e
qhN qef N
qehN qefN ]2
< 0:
(28)
In sum, domestic export volume is increasing in the trade cost that confronts foreign exports and
decreasing in the trade cost that faces domestic exports.
We can similarly derive long-run comparative statics …ndings for foreign export volumes. De…n13
ing the foreign country’s export volume as
E
N
( ; )
nN
qfN ( ; );
f ( ; )e
(29)
we then have
@E
N(
; )
@
= nN
f ( ; )
@ qefN ( ; )
@
+ qefN ( ; )
@nN
f ( ; )
@
> 0;
where the inequality follows from (25) and (19). Using (25) and (19), we …nd that
@E
=
N(
; )
@
N eN ((e
nN
q
e
qf N )2 + (e
qfN )2 ) + nN
efN qef N ((e
qhN )2 + (e
qhN )2 ) + qefN qehN (e
qhN qefN + qehN qef N )
f h q
h
h q
[e
qhN qef N
qehN qefN ]2
(30)
> 0:
Finally, we consider how foreign export volume varies with the trade cost that foreign exporters
incur. We thus compute
@E
N(
@
; )
= nN
f ( ; )
@ qefN ( ; )
@
+ qefN ( ; )
@nN
f ( ; )
@
< 0;
where the inequality follows from (25) and (18). Referring to (25) and (18), we have that
@E
N(
@
; )
=
nN
qhN )2 ((e
qf N )2 + (e
qfN )2 ) + (e
qfN )2 (1 + nN
qhN )2 + (e
qhN )2 )
f (e
h )((e
[e
qhN qef N
qehN qefN ]2
< 0:
(31)
In sum, foreign export volume increases when the trade cost facing domestic exports rises and
decreases when the trade cost facing foreign exports rises.
A case of particular interest arises when
=
markets. At a symmetric point, we have that qef
so that trade policies are symmetric across
N
N
= qehN , qefN = qehN and nN
f = nh . Under
symmetry, we may thus express all magnitudes in terms of domestic variables and derive simpler
expressions. In particular, at a symmetric point, we may simplify (27) and (30) as follows:
2e
q N qeN [nN ((e
q N )2 + (e
qhN )2 ) + (e
qhN )2 ]
@E N ( ; )
@E N ( ; )
=
= h h h Nh 2
> 0:
@
@
[(e
qh )
(e
qhN )2 ]2
(32)
Likewise, at a symmetric point, we may simplify (28) and (31) to get:
@E N ( ; )
@E N ( ; )
=
=
@
@
Note that (17) yields qhN
that
qhN =
((e
qhN )2 + (e
qhN )2 )[nN
qhN )2 + (e
qhN )2 (1 + nN
h (e
h )]
< 0:
N
N
[(e
qh )2 (e
qh )2 ]2
at a symmetric point, and so qhN
> 0.
14
(33)
qhN > 0 under our assumption
3
Unilateral and E¢ cient Trade Policies
With the key properties of the Cournot delocation model now developed, we are ready to consider
the determination of trade policies. We begin by de…ning national welfare. We then ask whether
a country could gain by introducing a slight departure from free trade in exactly one of its trade
policies. Venables (1985) considers this question as well, and we re-state his results regarding
unilateral departures from free trade here. In particular, we …nd that a country always gains from
introducing a slight import tari¤, provided only that the other country’s trade policies are such
that in each market the trade cost is positive and trade is not prohibited. Further, a country gains
by introducing a small export subsidy, if all other policies in both countries are set at free trade.
Finally, the introduction of an import tari¤ or an export subsidy also leads to a reduction in the
welfare of the other country, if all policies in both countries are initially set at the free-trade level.
We also establish the novel …nding that free-trade policies (i.e.,
the linear model studied
3.1
With
=
= ) are in fact e¢ cient in
here.7
Welfare Functions
> 0 representing the transport cost, we let
+ th + tf denote the total trade cost
imposed on foreign exports, where th is the (speci…c) domestic import tari¤ and tf is the (speci…c)
foreign export tari¤. Likewise, the total trade cost imposed on domestic exports is
+ th + tf ,
where th is the (speci…c) domestic export tari¤ and tf is the (speci…c) foreign import tari¤.
When evaluating trade policies, we assume that the domestic and foreign governments maximize
their respective long-run national incomes. In the long run, pro…ts are driven to zero, and national
income is simply the sum of consumer surplus and net tari¤ revenue. Letting CS(PeN ( ; )) denote
domestic consumer surplus in the long-run equilibrium, the domestic government thus maximizes
G( ; ; th ; th )
(34)
= CS(PeN ( ; )) + th nN
qfN ( ; ) + th nN
qhN ( ; )
f ( ; )e
h ( ; )e
= CS(PeN ( ; )) + th E
where CS 0 (PeN ( ; )) =
D(PeN ( ; ))
N
( ; ) + th E N ( ; );
(1
PeN ( ; )). Similarly, letting CS (Pe
N(
; ))
denote foreign consumer surplus, the foreign government maximizes
G ( ; ; tf ; t f )
= CS (Pe
7
= CS (Pe
(35)
N
( ; )) + tf nN
qhN ( ; ) + tf nN
qfN ( ; )
h ( ; )e
f ( ; )e
N
( ; )) + tf E N ( ; ) + tf E
N
( ; );
Markusen and Venables (1988, p. 315, Result 5) report that free trade is e¢ cient in a free-entry linear-demand
Cournot segmented-markets setting, where the products of di¤erent countries are not perfect substitutes and transport
costs between countries are absent. We are unaware of a result that establishes the e¢ ciency of free trade in this
setting when products are perfect substitutes and transport costs exist, as in the environment we consider here.
15
where CS 0 (Pe
3.2
N(
; )) =
D (Pe
N(
; ))
(1
Introduction of a Small Import Tari¤
Pe
N(
; )).
Now let us suppose that the domestic country initially adopts free trade with its import and export
tari¤s. With respect to foreign trade policies, we assume for the moment only that the foreign
government’s trade policies are such that the trade cost is positive (i.e.,
prohibited (i.e., E
N(
> 0) and trade is not
; ) > 0). From this starting point, would the domestic government gain
by slightly increasing its import tari¤? To answer this question, we use (34) and compute
dG
=
dth
D(PeN ( ; ))
@ PeN ( ; )
+E
@
N
( ; ) + th
@E
N(
; )
@
+ th
@E N ( ; )
:
@
(36)
Under our supposition that the domestic country is initially adopting a free-trade policy with
respect to its import and export tari¤s, the last two terms in (36) disappear. We may thus rewrite
(36) as
dG
=
dth
D(PeN ( ; ))
@ PeN ( ; )
+E
@
N
( ; ) > 0;
(37)
where the inequality follows since D(PeN ( ; )) > 0, E N ( ; ) > 0 under our assumption that
trade is not prohibited, and @ PeN ( ; )=@ < 0 by (20) under our assumption that trade costs are
positive. Thus, with the …rm-delocation e¤ect giving @ PeN ( ; )=@ < 0, we see that a positive
import tari¤ is optimal for the domestic country. Intuitively, the import tari¤ generates domestic
entry and thus a lower domestic price, which raises consumer surplus. As well, a positive import
tari¤ raises tari¤ revenue relative to the free-trade benchmark.
Consider now the impact of a small domestic import tari¤ on the foreign country. To this end,
we use (35) and compute
dG
=
dth
D (Pe
N
( ; ))
@ Pe
N(
; )
@
+ tf
@E N ( ; )
@E N ( ; )
+ tf
:
@
@
(38)
Now, if we suppose that the foreign country also initially adopts a free-trade policy with respect to
its import and export tari¤s, then the last two terms in (38) disappear. We may then rewrite (38)
as
dG
=
dth
D (Pe
N
( ; ))
@ Pe
N(
@
; )
< 0;
(39)
where the inequality follows at global free trade, since under these policies D (Pe N ( ; )) > 0
and trade costs are positive so that @ Pe N ( ; )=@ > 0 by (23). The latter e¤ect is simply the
…rm-delocation e¤ect: a higher domestic import tari¤ causes exit in the foreign country to such a
degree that the foreign price rises. In other words, starting with all policies in both countries set
at free trade, the introduction of a small domestic import tari¤ raises the foreign price and thus
harms foreign welfare by reducing foreign consumer surplus.
Following Venables (1985), we may conclude as follows:
16
Proposition 1: If both countries initially adopt a policy of free trade with respect to their imports
and exports, then the introduction of a small import tari¤ by the domestic government generates a
welfare gain for the domestic country and a welfare loss for the foreign country.
Of course, we could similarly argue that the introduction of a small import tari¤ by the foreign
government generates a welfare gain for the foreign country and a welfare loss for the domestic
country.
3.3
Introduction of a Small Export Subsidy
We consider next the introduction of a small export subsidy. Any e¤ect of a small export subsidy
is the same as that of a small export tari¤, once the sign of the e¤ect is reversed. Using (34), we
compute that
dG
=
dth
D(PeN ( ; ))
@ PeN ( ; )
@E N ( ; )
@E N ( ; )
+ E N ( ; ) + th
+ th
:
@
@
@
(40)
If the domestic country starts at free trade with respect to its import and export policies, we thus
…nd that the last two terms in (40) again disappear, and so we get
dG
=
dth
D(PeN ( ; ))
@ PeN ( ; )
+ E N ( ; ):
@
(41)
Assuming that the foreign trade policies are nonprohibitive and such that trade costs are positive,
we have that D(PeN ( ; )) > 0; @ PeN ( ; )=@ > 0 by (21), and E N ( ; ) > 0. Referring to
(41), we thus see that the introduction of a small export tari¤ has competing e¤ects on domestic
welfare: the export tari¤ induces exit and thereby a higher domestic price, which reduces consumer
surplus, but it also generates additional tari¤ revenue relative to the free-trade benchmark.
To sign the expression in (41), we use D(PeN ( ; )) = nN
efN ; (26) and (21) and …nd
ehN + nN
f q
h q
that, at free-trade domestic policies,
dG
=
dth
qehN qefN
N e N]
[e
q f N nN
f + nh q
h
[e
qhN qef N
where the inequality follows under our assumptions that
qehN qefN ]
< 0;
> 0 and
> 0. Thus, starting from free-
trade domestic policies and so long as the trade policies of the foreign country are non-prohibitive
and such that trade costs are positive, the domestic government gains when it introduces a small
export subsidy. In this model, therefore, when a small export subsidy is introduced, the bene…t to
domestic consumers of a lower domestic price (due to the …rm-delocation e¤ect) exceeds the loss
in tari¤ revenue.
We turn next to consider the implications of a small export tari¤ for the foreign country. To
17
this end, we use (35) and compute
dG
=
dth
D (Pe
N
( ; ))
@ Pe
N(
; )
@
+ tf
@E N ( ; )
@E N ( ; )
+ tf
:
@
@
(42)
If we now suppose that the foreign country also initially adopts a free-trade policy with respect to
its import and export tari¤s, then the last two terms in (42) disappear. Under this supposition, we
may rewrite (42) as
dG
=
dth
D (Pe
N
( ; ))
@ Pe
N(
; )
@
> 0;
(43)
where the inequality in (43) follows at global free trade since then D (Pe N ( ; )) > 0 and trade
costs are positive so that @ Pe N ( ; )=@ < 0 by (22). The latter e¤ect is again the …rm-delocation
e¤ect: a higher domestic export tari¤ induces su¢ cient entry in the foreign country that the
foreign price falls and foreign consumer welfare rises. Equivalently, starting at global free trade,
the introduction of a small export subsidy by the domestic country results in a reduction in the
welfare of the foreign country, since it induces foreign exit and thereby a higher foreign price and
thus lower foreign consumer surplus.
Following Venables (1985), we may conclude as follows:
Proposition 2: If both countries initially adopt free-trade policies with respect to their imports and
exports, then the introduction of a small export subsidy by the domestic government generates a
welfare gain for the domestic country and a welfare loss for the foreign country.
Again, we could similarly argue that the introduction of a small export subsidy by the foreign
government generates a welfare gain for the foreign country and a welfare loss for the domestic
country.
3.4
E¢ cient Trade Policies
Finally, we consider the impact on joint welfare of small deviations from global free trade. If both
countries initially adopt free-trade policies with respect to imports and exports, and the domestic
country introduces a small import tari¤, then we may use (37) and (39) to calculate that the e¤ect
on joint welfare, G + G , is
dG dG
+
dth
dth
=
D(PeN ( ; ))
(44)
@ PeN ( ; )
+E
@
N
( ; )
D (Pe
N
( ; ))
@ Pe
N(
; )
@
where the …nal equality follows after using D(PeN ( ; )) = nN
ehN + nN
efN , D (Pe
h q
f q
nN
ehN
h q
+ nN
ef N ,
f q
= 0;
N(
; )) =
(20), (29) and (23). Thus, assuming that all other policies are set at free trade, we
see from (44) that the e¢ cient import tari¤ for the domestic government is free trade. Similarly,
18
under these assumptions, the e¢ cient import tari¤ for the foreign government is free trade.8
The next step is to make sure that free trade is the e¢ cient export policy for the domestic
country, when all other policies are set at free trade. Using (37) and (39), we …nd that at global
free trade the impact on joint welfare of the introduction of a small export tari¤ imposed by the
domestic government is
dG dG
+
dth
dth
(45)
D(PeN ( ; ))
=
@ PeN ( ; )
+ EN ( ; )
@
D (Pe
N
( ; ))
N e N , D (P
e
where the …nal equality uses D(PeN ( ; )) = qef N nN
f + nh q
h
@ Pe
N(
N(
@
; )
= 0;
; )) = nN
ehN + nN
ef N ,
h q
f q
(21), (26) and (22). Assuming that other policies are set at free trade, we see from (45) that the
domestic government maximizes joint welfare by adopting an export policy of free trade. Similarly,
under these assumptions, the foreign government maximizes joint welfare by adopting an export
policy of free trade.9
Thus, for our linear model, a policy of free trade in import and export policies by both countries
is e¢ cient. Of course, an e¢ cient outcome can be achieved with other trade-policy vectors as well.
In particular, we note that joint welfare ultimately depends only on the total trade costs,
and
.
To see this, observe that
J( ; )
G( ; ; th ; th ) + G ( ; ; tf ; tf )
= CS(PeN ( ; )) + th E
+CS (Pe
N
N
( ; ) + th E N ( ; )
( ; )) + tf E N ( ; ) + tf E
= CS(PeN ( ; )) + CS (Pe
Since free trade yields
=
=
=
=
N
( ; )) + (
N
( ; )
)E
N
)E N ( ; )
( ; )+(
and is e¢ cient, any combination of trade policies that delivers
is also e¢ cient, and only such combinations are e¢ cient.10 There is thus a continuum
of e¢ cient trade policies, where along any one trade channel any subsidy by one country is exactly
o¤set by a tari¤ from the other country.
8
Di¤erentiating (36) and (38) with respect to th and evaluating the sum of the resulting expressions at global free
N
trade yields @E @( ; ) , which by (33) is strictly negative. Hence the second-order condition associated with (44) is
satis…ed.
9
Di¤erentiating (40) and (42) with respect to th and evaluating the sum of the resulting expressions at global free
N
trade yields @E @ ( ; ) , which by (33) is strictly negative. Hence the second-order condition associated with (45) is
satis…ed.
10
To formally establish that
=
=
is e¢ cient when and
are jointly selected, we observe from (44)
and (45) that @J(@ ; ) = 0 = @J(@ ; ) when
=
= , and we con…rm that the corresponding second-order
conditions are then satis…ed. In particular, the second-order conditions hold at =
=
when and
are
jointly selected if the Jacobian matrix associated with the system of …rst-order conditions is negative de…nite. The
2
N
N
2
; )
; )
preceding two footnotes imply that, when =
= , @ J(
= @E @( ; ) = @E @ ( ; ) = @ J(
< 0. We
@ 2
@ 2
N
@ 2 J( ; )
= @E @( ; )
@ @
2
@ J( ; ) @ J( ; )
( @ @J(@ ; ) )2 >
@ 2
@ 2
further …nd that
that
2
2
=
@E N (
@
0 at
=
; )
=
when
=
= . Using (33) and (32), we may then con…rm
under our assumption that
19
> 0.
We may thus conclude as follows:
Proposition 3: The e¢ ciency frontier is characterized by combinations of trade policies that
deliver zero trade taxes on all trade (i.e.,
=
= ); in particular, global free trade ( th = th =
tf = tf = 0) is e¢ cient.
Together, Propositions 1, 2 and 3 indicate that global free trade is e¢ cient and yet not a Nash
equilibrium in trade policies. Our next task is to characterize the Nash equilibrium trade policies.
4
Nash Trade Policies
At this point, we know that free trade is e¢ cient, and we know that from this starting point each
country has a unilateral incentive to impose an import tari¤ and an export subsidy. These …ndings
thus provide one perspective as to why governments might seek an agreement under which ceilings
are imposed on import tari¤s and export subsidies. We next consider the Nash equilibrium in trade
policies, and we show that governments use import and export tari¤s in a Nash equilibrium. This
result is novel to the literature and provides a richer perspective on the treatment of import tari¤s
and export subsidies in trade agreements. In particular, an e¢ ciency enhancing trade agreement
would place a ceiling on export subsidies only once import tari¤s have been reduced through
negotiations to a level that is su¢ ciently close to free trade. As explained in the Introduction, this
richer perspective thus provides one interpretation of the introduction of the SCM Agreement into
the WTO in 1995, after the completion of several earlier negotiation rounds that led to substantial
reductions in import tari¤s.
To characterize Nash equilibrium trade policies in the Cournot delocation model, we are led
to consider the tari¤ reaction functions for the domestic and foreign countries, respectively. The
domestic …rst-order conditions for th and th are given by dG=dth = 0 and dG=dth = 0, respectively,
and may be analyzed using (36) and (40) above.11 Furthermore, since the two countries are symmetric, we may focus on a symmetric Nash equilibrium, in which the domestic Nash import tari¤
equals the foreign Nash import tari¤, and the domestic Nash export tari¤ equals the foreign Nash
export tari¤. Thus, we can focus on the domestic tari¤ reaction functions and the determination
N
of the domestic Nash import tari¤, tN
h and Nash export tari¤, th .
To this end, we …rst use (40) and (36) and subtract the domestic …rst-order condition for th
11
The second-order conditions for the domestic country’s import and export tari¤ selection hold at the Nash
2
2
@2G
@2G
@2G
G
equilibrium if @@tG
) > 0, where all expressions are evaluated with all tari¤s
( @t@h @t
2 < 0; @t 2 < 0 and ( @t2 )( @t 2 )
h
h
h
h
h
set at their Nash levels. The second-order conditions are di¢ cult to con…rm analytically, since the expressions (54)
and (55) that we derive below for the Nash tari¤ levels are implicit equations. (Recall that the numbers of …rms and
per-…rm quantities are functions of tari¤s.) Nevertheless, we can show that the second-order conditions must hold
at the Nash equilibrium when the quantity exported by each …rm, qeh , is su¢ ciently small. This will be the case if
the transportation cost, , is su¢ ciently large. In addition, we have con…rmed that the second-order conditions are
satis…ed at the Nash equilibrium for a variety of speci…cations for the model’s parameters, c; F and .
20
from the domestic …rst-order condition for th . This yields
0 =
dG
dth
dG
dth
(46)
= D(PeN ( ; ))[
@ PeN ( ; )
@
where we use symmetry to impose E
@E N (
; )=@ = @E
N(
; )=@
N(
@ PeN ( ; )
] + [tN
h
@
thN ][
@E N ( ; )
@
; ) = E N ( ; ), @E N ( ; )=@
@E N ( ; )
];
@
= @E
N(
; )=@ and
.
To further simplify (46), we compute @ PeN ( ; )=@
@ PeN ( ; )=@ and @E N ( ; )=@
@E N ( ; )=@ at a symmetric point. Using (21) and (20) and simplifying, we …nd
@ PeN ( ; )
@
At a point of symmetry, therefore,
@ PeN ( ; )
@
qef N qehN + qefN qehN
@ PeN ( ; )
:
= N N
@
qehN qefN ]
[e
qh qef
qe N
@ PeN ( ; )
= N h N > 0;
@
qeh
qeh
where the inequality follows since we have from (17) that qehN
symmetric point, under the assumption that
@E N ( ; )
=
@
+nf ( + )
1+nh +nf
=
> 0 at a
> 0. Next, we may similarly use (28) and (27) and
establish after simpli…cation that, at a symmetric point,
@E N ( ; )
@
qehN =
(47)
qhN )2
qhN )2 ] + (e
qhN )2 + (e
nN
h [(e
< 0;
[e
qhN qehN ]2
where the inequality again follows at a symmetric point under our assumption that
(48)
> 0.
We may now return to our “subtraction”equation (46) and make the substitutions just derived
in (47) and (48). After making these substitutions and simplifying, we get, for a symmetric point,
that
0=
dG
dth
qehN
dG
N
N
= nN
[e
q
+
q
e
][
]
h h
h
dth
qehN qehN
[tN
h
thN ]
Thus, at a symmetric Nash equilibrium, we conclude that
tN
h
thN =
nN
qhN )2 + (e
qhN )2 ] + (e
qhN )2
h [(e
:
[e
qhN qehN ]2
nN
qhN + qehN ]e
qhN [e
qhN qehN ]
h [e
:
nN
qhN )2 + (e
qhN )2 ] + (e
qhN )2
h [(e
N
Importantly, (49) con…rms that tN
ehN
h > th , provided that q
qehN =
(49)
> 0. In other words, the
domestic import tari¤ is greater than the domestic export tari¤ precisely because of the local-market
bias in …rm sales.
Our next step is to use (36) and (40) and add the domestic …rst-order condition for th to the
21
domestic …rst-order condition for th . We obtain
0 =
=
dG
dG
+
dth dth
(50)
D(PeN ( ; ))[
N
@ PeN ( ; ) @ PeN ( ; )
@E N ( ; )
N @E ( ; )
] + 2E N ( ; ) + [tN
];
+
+
h + th ][
@
@
@
@
where we use symmetry to impose E
@E N ( ; )=@ = @E
N(
; )=@
N(
; ) = E N ( ; ), @E N ( ; )=@
N(
; )=@ and
.
To further analyze (50), we compute @ PeN ( ; )=@ + @ PeN ( ; )=@
@E N ( ; )=@
= @E
and @E N ( ; )=@ +
at a symmetric point. Using (20) and (21) and simplifying, we …nd that
qehN [e
qf N qefN ]
@ PeN ( ; ) @ PeN ( ; )
:
+
= N N
@
@
qehN qefN ]
[e
qh qef
At a point of symmetry, therefore,
qe N
@ PeN ( ; ) @ PeN ( ; )
+
= N h N > 0:
@
@
[e
qh + qeh ]
(51)
Similarly, we may use (27) and (28) and establish after simpli…cation that, at a symmetric point,
@E N ( ; ) @E N ( ; )
+
=
@
@
qhN )2
qhN )2 ] + (e
qhN )2 + (e
nN
h [(e
< 0:
[e
qhN + qehN ]2
(52)
At this point, we may return to our “addition” equation (50) and make the substitutions just
derived in (51) and (52). After making these substitutions and simplifying, we get, for a symmetric
point, that
0=
dG
dG
ehN
+
= nN
h q
dth dth
N
[tN
h + th ]
qhN )2
qhN )2 ] + (e
qhN )2 + (e
nN
h [(e
:
[e
qhN + qehN ]2
Thus, at a symmetric Nash equilibrium, we conclude that
t h + th =
nN
ehN [e
qhN + qehN ]2
h q
> 0:
nN
qhN )2 + (e
qhN )2 ] + (e
qhN )2
h [(e
(53)
Importantly, (53) indicates that, at the Nash equilibrium, the total trade tax and thus the total
trade cost is positive:
=
> 0 indeed holds.
At this point, we may add (49) and (53) to obtain
tN
h =
nN
qhN + qehN )e
qhN qehN
h (e
> 0:
nN
qhN )2 + (e
qhN )2 ] + (e
qhN )2
h [(e
(54)
This implicit equation tells us that the Nash import tari¤ must be positive. Using (53) and (54)
22
and simplifying, we may now recover the Nash export policy as
thN =
nN
qhN )2 (e
qhN + qehN )
h (e
> 0:
qhN )2
qhN )2 ] + (e
qhN )2 + (e
nN
h [(e
(55)
This implicit equation tells us that the Nash export tari¤ must be positive as well.
We may now conclude as follows:
Proposition 4: In a (symmetric) Nash equilibrium in trade policies, the Nash import and export
tari¤ s are both positive, with the Nash import tari¤ being the larger of the two.
Comparing Propositions 3 and 4, we see immediately that Nash trade policies are ine¢ cient in
the linear Cournot delocation model.12 In particular, using the fact that
and
take symmetric
values in both the e¢ cient free-trade benchmark and the Nash equilibrium, we may conclude from
(52) that too little trade occurs under Nash trade policies.
It is also interesting to compare our characterization in Proposition 4 of the Nash equilibrium
trade policies with Propositions 1 and 2 of the previous section, where we show that a country
can gain by unilaterally departing from global free trade and introducing a small import tari¤ or a
small export subsidy. Viewed from this perspective, our …nding of a positive Nash import tari¤ is
perhaps not surprising. Our …nding of a positive Nash export tari¤, however, is more surprising.
How can we reconcile the gain that a country experiences when departing from global free trade
and introducing a small export subsidy with the …nding that the Nash equilibrium entails an export
tari¤? We address this question in the next section.
5
Interpretation of Trade Policy Findings
We now have two sets of …ndings. First, starting at global free trade, each country has an incentive
to introduce a small import tari¤ or alternatively a small export subsidy. Second, in a Nash
equilibrium, each country uses an import tari¤ and an export tari¤. We consider now how to
explain these seemingly contradictory …ndings.
When choosing its trade policy, a government seeks to maximize the sum of consumer surplus
and tari¤ revenue. Consumer surplus is governed by the consumption price. Focusing for simplicity
on the domestic country, consider then the iso-price relationship PeN ( ; ) = k for some initial value
k. We can think of this relationship as generating an iso-price tari¤ function,
( ; k), which has
positive slope. In particular, using (20) and (21), we …nd that
@
@
12
=
@ PeN ( ; )=@
@ PeN ( ; )=@
=
qefN
qef N
< 1;
(56)
In Bagwell and Staiger (2009), we consider a more general representation of the Cournot delocation model and
establish that Nash trade policies are ine¢ cient. In that paper, however, we do not o¤er a detailed analysis of the
Nash trade policies. For example, we do not consider there the sign of the Nash export policy.
23
+ nN
h ( +
where the inequality holds so long as
and
) > 0 and thus under our assumption that
are positive. An interesting observation is that a government can adjust its import and
export tari¤s along the upward-sloping iso-price tari¤ function,
( ; k), without impacting the
surplus that its consumers enjoy on the associated good. In particular, there exists a tari¤-revenuemaximizing way of delivering any given local price and thus consumer surplus.
Suppose that the foreign government has selected a pair of tari¤s, tf and tf , which along with
an initial pair of domestic tari¤s, th and th , generate values and
and thereby a domestic
N
e
local price P ( ; ) = k. Building on the observation made above, we may now ask which pair
of domestic tari¤s maximizes domestic tari¤ revenue, when the local price is taken as …xed. The
associated program is
N
max T R(th ; th ; tf ; tf ) = th E
th ;th
s:t: PeN ( ; ) = k;
or equivalently
= th + tf + ;
N
max T R(th ; th ( ; tf ; k); tf ; tf ) = th E
th
= tf + th +
( ( ; k); ) + th ( ; tf ; k)E N ( ( ; k); );
where with tf and tf …xed the induced value for
as th and thereby
( ; ) + th E N ( ; )
( ; k) is achieved via appropriate selections for th
is varied. In particular, the induced value for th is th ( ; tf ; k)
,
( ; k) tf
where we suppress the dependence on
in the functional notation. The domestic Nash tari¤s, for
example, must solve this program when k = PeN ( N ; N ).
We can write the …rst-order condition for this program as
dT R(th ; th ( ; tf ; k); tf ; tf )
dth
= [E
N
+th [
where we utilize (56).
( ( ; k); ) + E N ( ( ; k); )
@E
@
N
qefN
qef N
+
@E
@
N
qefN
qef N
] + th ( ; tf ; k)[
]
(57)
N
@E N qef
@E N
+
] = 0;
@
@
qef N
Suppose now that we initially place the domestic tari¤s at free trade, while …xing the foreign
tari¤s at any non-prohibitive level consistent with positive trade costs. These policies induce a
domestic free-trade price PeN (tf + ; tf + ) = k0 . Thus, at this starting point, th = th (tf +
; tf ; k0 ) = 0. Starting from here, we may ask whether the domestic government would like to
raise its import tari¤, th , while increasing its export tari¤, th , a comparable amount as de…ned
by (56) that serves to preserve the initial domestic free-trade price. The …rst-order condition
(57) for our program, evaluated at th = 0 = th , indicates that the domestic country would gain
from such an adjustment, since it would enjoy an increase in tari¤ revenue with no change in
consumer surplus. In particular, the gain in domestic tari¤ revenue and thus domestic welfare is
E
N(
( ; k); ) + E N ( ( ; k); )e
qfN =e
qf N > 0:
24
We may summarize the result of this variation as follows:
Proposition 5: Suppose the domestic tari¤ s are initially placed at free trade, with the foreign
tari¤ s …xed at any non-prohibitive level consistent with positive trade costs. From this starting
point, suppose further that the domestic government undertakes a slight increase in its import tari¤
while increasing its export tari¤ a comparable amount as de…ned by (56) that serves to preserve the
initial domestic free-trade price. Then the domestic country enjoys a welfare gain, since its tari¤
revenue increases while its consumer surplus is unaltered.
It is interesting to compare this unilateral departure from free trade with those analyzed by Venables
(1985) and in the previous section. As shown in Propositions 1 and 2, the introduction of a small
import tari¤ and the introduction of a small export subsidy each serve to raise domestic welfare.
Notice, though, that these variations entail simultaneous changes in consumer surplus and tari¤
revenue. By contrast, the variation that we consider in Proposition 5 entails a simultaneous increase
in the import and export tari¤s that preserves consumer surplus and isolates the tari¤-revenue
e¤ect.13
This discussion suggests a way to reconcile the …nding that the optimal unilateral export policy
is an export subsidy with the …nding that the Nash equilibrium entails an export tax. In particular,
as suggested by Proposition 2, let us suppose that the domestic import tari¤ and all foreign tari¤s
are initially set at free trade, and let us then place the domestic export policy at the optimal
unilateral export subsidy. From here, we can imagine a further variation in which we both raise
the domestic import tari¤ and reduce the domestic export subsidy so as to maintain the domestic
local price. If this adjustment increases tari¤ revenue, then we could even end up with a preferred
situation for the domestic country in which import and export tari¤s are positive. In the lineardemand case at least, the Nash equilibrium tari¤s can be understood in this way. By considering
only one policy change at a time, the variations considered by Venables (1985) and featured in
Propositions 1 and 2 do not permit such simultaneous adjustments in import and export policies.
Proposition 5 highlights the potential value to a country of simultaneously making its import
and export policies more restrictive.14 This orientation suggests that a country’s import and export
tari¤s are at least in some cases complementary with respect to their e¤ects on tari¤ revenue. In
turn, this line of thought provides some additional intuition for why the Nash import and export
tari¤s are indeed positive.
To further develop this intuition, we now formally identify a novel tari¤ -complementarity effect that arises in the Cournot delocation model of trade policy.15
In particular, recall that
13
The variation we consider here clearly applies for a general class of demand functions, since the result reported in
Proposition 5 requires only that
is upward sloping. Also, and as Proposition 5 a¢ rms, the result of the variation
considered here holds for a wide range of possible foreign tari¤ speci…cations.
14
In fact, the …nding reported in Proposition 5 can be strengthened so as to allow for any initial domestic trade
policies satisfying th 0 and th 0, suggesting that the attractiveness of raising the restrictiveness of both import
and export policies in this fashion may be quite broad.
15
The tari¤-complementarity e¤ect identi…ed here entails a complementary relationship between a country’s import
and export tari¤s, for the same good. This e¤ect is thus distinct from previously identi…ed tari¤-complementarity
25
T R(th ; th ; tf ; tf ) = th E
N(
; ) + th E N ( ; ): Consider now the cross derivative of domestic tari¤
revenue with respect to changes in the domestic tari¤ instruments, th and th . We …nd that
@2T R
@E N
@E
=
+
@th @th
@
@
N
+ th
@2EN
@2E
+ th
@ @
@ @
N
:
(58)
Using (27) and (30), and assuming that foreign tari¤s are non-prohibitive and such that trade costs
are positive, we know that @E N =@ +@E
N =@
> 0. Thus, at least in the neighborhood of domestic
free trade, we have from (58) that there exists a clear tari¤-complementarity e¤ect: @ 2 T R=@th @th >
0 when th = 0 = th .
We now summarize our …nding to this point as regards the tari¤-complementarity e¤ect:
Proposition 6: For domestic tari¤ s su¢ ciently close to free trade, the domestic import and export
tari¤ s exert a complementary e¤ ect on domestic tari¤ revenue, provided that foreign tari¤ s are
non-prohibitive and such that trade costs are positive.
The idea behind the tari¤-complementarity e¤ect is as follows.16 When a small export tari¤,
th ; is introduced, tari¤ revenue is enjoyed on those units that are exported. If a small import tari¤
is then introduced as well, domestic entry occurs and so more domestic units are exported. Thus,
an import tari¤ can increase the marginal revenue of an export tari¤. Indeed, this must be the
case when the export tari¤ begins at free trade and is then raised. Similarly, if we were to …rst
introduce an import tari¤, then import tari¤ revenue would be enjoyed on imported units; further,
the volume of imports would only grow were an export tari¤ introduced as well, since the export
tari¤ would trigger foreign entry and thus a greater volume of foreign exports. In this way, an export
tari¤ can increase the marginal revenue of an import tari¤. The described tari¤-complementarity
e¤ect is general and is not limited to the linear-demand setting; however, when tari¤s begin at
values di¤ering from free trade, then the marginal revenue associated with an initial tari¤ hike is
determined in part by the e¤ect of the hike on the volume of trade on which the initial tari¤ is
applied. A tari¤ hike on the other channel can then alter marginal revenue on the initial channel by
altering the rate at which the initial tari¤ hike a¤ects trade volume on the initial channel. Hence,
when we begin at values di¤ering from free trade, new e¤ects come into play that are associated
with the cross derivatives of the export volume functions.17
The tari¤-complementarity e¤ect identi…ed in Proposition 6 provides additional intuition for
the fact that both import tari¤s and export tari¤s are positive in a Nash equilibrium. In e¤ect,
e¤ects that concern complemetary relationships between the (discriminatory) import tari¤s that a country applies to
di¤erent suppliers of an import good (Bagwell and Staiger, 1999b) or between the import tari¤s of di¤erent countries
which import a common good (Bagwell and Staiger, 1997).
16
For domestic tari¤s su¢ ciently close to free trade, and provided that foreign tari¤s are non-prohibitive and such
that trade costs are positive, we can show that domestic import and export tari¤s also exert a complementary e¤ect
2
G
on domestic welfare (i.e., @t@h @t
> 0): We emphasize the complementary e¤ect that domestic tari¤s exert on domestic
h
tari¤ revenue, in order to further develop the intuition underlying Proposition 5.
2 n
2
n
17
We can show that, at a point of symmetry, @@ @E = @@ E@
< 0. At a symmetric point with positive tari¤s,
2
@ TR
therefore, we see from (58) that the sign of @th @t involves competing e¤ects.
h
26
the joint use of import tari¤s and export tari¤s is attractive to governments in the linear Cournot
delocation model, because a tax on trade in one direction encourages trade in the other direction
on which the other trade tax can then collect revenue.
6
Politically Optimal Trade Policies
In the Cournot delocation model, international externalities travel from one country’s trade policy
to another country’s welfare. As a consequence, and as noted above, Nash trade policies are
ine¢ cient. In Bagwell and Staiger (2009), we argue at a general level that unilateral trade policies
would be e¢ cient if governments were not motivated by the terms-of-trade implications of their
respective trade policy selections. In this sense, the ine¢ ciency attributable to the terms-of-trade
externality is the “problem” that a trade agreement can be designed to solve. To make this point,
we represent welfare in terms of local and world prices and then de…ne the politically optimal
policies as the (import and export) trade policies that governments would choose if they were not
motivated by the terms-of-trade implications of their respective selections. The central …nding is
that the politically optimal policies are e¢ cient.
In this section, we utilize the additional structure that the linear Cournot delocation model
provides and characterize the speci…c trade policies that are politically optimal in this model.
Given that politically optimal trade policies are known to be e¢ cient, we know from Proposition 3
that politically optimal trade policies must impose a net trade tax of zero (i.e.,
=
= ). Thus,
if the politically optimal policies were to involve an import tari¤ along one channel of trade, then
an o¤setting export subsidy would be required along this same channel. We establish in this section
that a (symmetric) political optimum exists for the linear Cournot delocation model in which global
free trade is achieved (i.e., each country adopts a policy of free trade with respect to its imports
and exports). For the linear Cournot delocation model, therefore, if countries were not motivated
by the terms-of-trade implications of their policies, then it is reasonable to expect that they would
achieve e¢ ciency by adopting the speci…c policy vector of global free trade. After establishing this
result, we then comment brie‡y at the end of this section on the implications of this …nding for the
interpretation of the WTO SCM Agreement.
6.1
Welfare Functions
Our …rst task is to rewrite domestic and foreign welfare as functions of local and world prices. We
thus begin by de…ning the full set of local and world prices. Recall that the domestic and foreign
local prices may be respectively expressed as PeN ( ; ) and Pe N ( ; ). We may now de…ne the
following world prices: P wN (th ; ; ) PeN ( ; ) th and P wN (t ; ; ) Pe N ( ; ) t . We
f
thus de…ne
P wN (t
h;
f
; ) to represent the price of foreign exports on the world market (i.e., prior
to the imposition of the domestic import tari¤, th ), while we de…ne P
wN (t
f;
; ) to represent the
price of domestic exports on the world market (i.e., prior to the imposition of the foreign import
tari¤, tf ). Finally, it is convenient to consider a unit that will be exported and to de…ne its local
27
price in the exporting country as the price that remains once the import tari¤, export tari¤ and
transport cost are subtracted from its local price in the importing country. Speci…cally, we de…ne
the following local prices
Pe
RN ( ; )
R
N
N
( ; )
PeN ( ; )
( ; )
wN
=P
(tf ;
= P wN (th ;
; )
; )
th
tf
:
We note that RN ( ; ) may di¤er from PeN ( ; ), since markets are segmented.
R N ( ; ) may di¤er from Pe N ( ; ).18
Similarly,
We next represent …rm output, entry levels, and trade volumes as functions of local prices.
Let us start with the Cournot-Nash …rm quantities. Using = PeN ( ; ) R N ( ; ) and
=
N
N
e
P ( ; ) R ( ; ), and recalling that long-run Cournot-Nash …rm quantities may be expressed
as functions of the underlying total tari¤s, we may think of the Cournot-Nash quantities of …rms as
functions of local prices. Thus, in the domestic market, we may express Cournot-Nash quantities
as qehN (Pe N RN ; PeN R N ) = qehN ( ; ) and qefN (Pe N RN ; PeN R N ) = qefN ( ; ). Similarly,
in the foreign market, we have the following expressions: qe N (Pe N RN ; PeN R N ) = qe N ( ; )
h
h
and qef N (Pe
N
RN ; PeN
R
N)
= qef N ( ; ). Of course, local prices are themselves ultimately
determined by the tari¤ selections.
We may treat the numbers of …rms and also export volumes in a similar fashion. Using (15),
e N RN ; PeN R N ) =
we may represent the numbers of …rms as functions of local prices: nN
h (P
nN ( ; ) and nN (Pe N RN ; PeN R N ) = nN ( ; ). Likewise, using (26) and (29), we see that
h
f
f
export volumes can also be regarded as functions of local prices: E N (Pe
E N ( ; ) and E N (Pe N RN ; PeN R N ) = E N ( ; ).
RN ; PeN
N
R
N)
=
At this point, we have all of the ingredients for representing domestic and foreign welfares as
functions of the local and world prices that the respective tari¤ selections induce. Referring to (34),
we may now rewrite domestic welfare as
W (PeN ; RN ; P wN ; Pe
eN
eN
= CS(P ) + [P
+[P
wN
RN
N
;P
wN
]E
N
]E N (Pe
N
(Pe
N
P
N
;R
wN
)
(59)
N
R ;P
RN ; PeN
Notice that, for any …xed set of trade policies, W (PeN ; RN ; P wN ; Pe
18
eN
R
R
N
N
)
):
N ; R N ; P wN )
= G( ; ; th ; th ),
Using (20), we may now see that an import tari¤ has the traditional e¤ect of generating an improvement in
the importing country’s terms-of-trade. In particular, dP wN =dth = @ PeN ( ; )=@
1 < 0; thus, a higher domestic
import tari¤ reduces the world price of the imported unit and thereby generates a terms-of-trade gain for the domestic
country. At the same time, we may use (21) to see that an export tari¤ has a non-traditional e¤ect on the exporting
country’s terms of trade. Speci…cally, dP wN =dth = @ Pe N ( ; )=@
< 0; thus, a higher domestic export tari¤
reduces the world price of the exported unit and thereby generates a terms-of-trade loss for the domestic country.
An export subsidy thus generates a terms-of-trade gain for the exporting country. This novel.feature of the Cournot
delocation model is attributable to the …rm-delocation e¤ect. Of course, exactly analogous results apply for the
foreign country. For further discussion of the terms-of-trade e¤ects present in the Cournot delocation model, see
Bagwell and Staiger (2009).
28
since the local and world price variables in W are those which are induced by the tari¤ variables
represented in G. Similarly, referring to (35), we may now rewrite foreign welfare as
W (PeN ; RN ; P wN ; Pe
= CS (Pe
+[P
wN
N
) + [Pe
R
N
N
]E
N
P
N
;R
N
wN
]E N (Pe
(Pe
;P
N
wN
)
(60)
N
N
RN ; PeN
eN
R ;P
R
N
R
N
)
):
Just as for the domestic welfare expressions, we have that, for any …xed set of trade policies,
W (PeN ; RN ; P wN ; Pe N ; R N ; P wN ) = G ( ; ; tf ; tf ).
6.2
Political Optimum
We are now prepared to characterize politically optimal trade policies. We focus …rst on the
domestic country, who we suppose acts as if WP wN
0 and WP
0 when choosing its politically
wN
optimal trade policies. The …rst-order condition for politically optimal domestic import policy is
then
WPeN
@ PeN
@RN
+ WR N
+ WPe
@
@
WPeN
@RN
@ PeN
+ WR N
+ WPe
@
@
N
@ Pe
@
N
@ Pe
@
N
+ WR
N
@R
@
N
= 0:
(61)
Likewise, the …rst-order condition for the politically optimal domestic export policy is
N
+ WR
N
@R
@
N
= 0:
(62)
At this point, we have derived two conditions (i.e., (61) and (62)) with which to determine the
politically optimal levels of the two domestic trade-policy selections (i.e., th and th ). Of course,
we can derive two symmetric equations for the foreign country, and these equations can be used
to determine the politically optimal levels of the two foreign trade-policy selections. To keep the
analysis simple, however, we will focus here on the existence and characterization of a symmetric
political optimum, wherein tf = th and tf = th . With the symmetry requirement imposed, our
task is to characterize the values for th and th that satisfy (61) and (62).
In the Appendix, we use the analysis of the model developed in previous sections and establish
that (61) and (62) are uniquely satis…ed when th = th = 0.19 We may thus summarize our …ndings
in this section as follows:
Proposition 7: There exists a unique symmetric political optimum, and in this political optimum
each country practices free trade with respect to its import and export policies.
In short, if governments were not motivated by the terms-of-trade implications of their trade policies, then they would achieve an e¢ cient outcome; furthermore, in the linear Cournot delocation
19
We may also verify that the second-order conditions for the political optimum are satis…ed. In the Appendix, we
simplify and express the …rst-order conditions for the politically optimal domestic import and export policies as (66)
and (69). At global free trade, we may easily verify that the Jacobian matrix associated with these two …rst-order
conditions is the same as the Jacobian matrix associated with the …rst-order conditions for e¢ cient tari¤s. We show
above in footnote 10 that this matrix is negative de…nite.
29
model, they would in particular achieve e¢ ciency by individually setting each import and export
tari¤ equal to zero. Global free trade is thus the unique symmetric political optimum for this
model.
An implication of this …nding is that the prohibition of export subsidies contained in the WTO
SCM Agreement is compatible with the political optimum in this model. This feature strengthens
the ability of the linear Cournot delocation model to provide an interpretation of the treatment of
export subsidies in the GATT/WTO, given that other design features of the GATT/WTO can also
be interpreted as guiding governments toward e¢ cient politically optimal outcomes (see Bagwell
and Staiger, 1999a, 2009).
7
Conclusion
In this paper, we consider trade policies and agreements in the linear Cournot delocation model. We
have shown that this model is capable of delivering a potential e¢ ciency-enhancing interpretation
for WTO rules on export subsidies. This distinguishes the Cournot delocation model from other
formal analyses of the treatment of export subsidies in trade agreements, which as we have observed suggest that GATT/WTO e¤orts to reign in export subsidies may be best interpreted as an
ine¢ cient victory for exporting governments that comes at the expense of importing governments.
This raises the question whether the Cournot delocation model o¤ers a compelling rationale
for the GATT/WTO e¤orts to restrict the use of export subsidies. This question is not merely
academic. Many GATT/WTO disputes involve export subsidies, and some of the longest-running
disputes, and largest in terms of authorized retaliation, have centered on government programs that
were alleged to operate as export subsidies.20 So there is much at stake in assessing the “legitimacy”
of the SCM’s prohibition against export subsidies.
This question is ultimately an empirical one, since it boils down to whether the Cournot delocation model, or rather any of the other models that deliver the more skeptical view of the
GATT/WTO stance on export subsidies, better captures the forces that are relevant for understanding and interpreting the GATT/WTO. As a consequence, the question cannot be answered
here. But we mention several points that may be relevant in providing an eventual answer.
First, we have established our results in a linear-demand version of the Cournot delocation
model. This raises the obvious question whether the e¢ ciency-enhancing interpretation for WTO
rules on export subsidies would survive with general non-linear demands. This is a subtle question,
because linearity plays several roles in the model. On the one hand, in a companion paper (Bagwell
and Staiger, 2009) we establish that export subsidies have non-traditional (bene…cial) terms-of-trade
e¤ects for the exporting country in the Cournot delocation model even when demands are nonlinear, indicating that the essential beggar-thy-neighbor features of export subsidies that argues for
20
For example, the U.S.-EU civil aircraft dispute concerning government support for Boeing and Airbus, which
includes allegations of illegal export subsidies, has spanned a period of almost 25 years, while the largest level of
retaliation ever authorized in a GATT/WTO dispute concerned the U.S.-EU dispute over the U.S. FISC program,
which amounted to an export subsidy.
30
their restraint (see note 18) is not limited to a linear-demand setting. This suggests that the main
insights from the linear Cournot delocation model are likely to survive in some form with general
non-linear demands. On the other hand, when demands are non-linear, global free trade may not
be e¢ cient in this setting, and so whether the prohibition of export subsidies is compatible with the
e¢ cient political optimum then remains an open question. On balance, though, the assumption of
linear demands does not seem to be driving the case for restraining export subsidies on e¢ ciency
grounds that arises in the Cournot delocation model. Hence, evidence that the Cournot delocation
model with general non-linear demands has empirical relevance would lend support to the view of
GATT/WTO export subsidy agreements that we develop here.
Second, we have adopted the Cournot version of the …rm-delocation model formalized by Venables (1985), but Venables (1987) has also formalized the …rm-delocation e¤ect in a di¤erentiated
product monopolistic competition setting, a setting that has been used recently to explore features
of trade agreements in Ossa (2009) and also in Bagwell and Staiger (2009). This raises the question
whether the monopolistic competition version of the …rm-delocation model might also deliver an
e¢ ciency rationale for the prohibition of export subsidies. Here the answer is no. As established
in Bagwell and Staiger (2009), in that model, as in other formal analyses of export subsidies and
for the same reason, e¢ ciency requires that export subsidies should, if anything, be encouraged by
a trade agreement. Hence, it is the empirical relevance of the Cournot version of the delocation
model that is at issue here.
And …nally, we emphasize that there may of course not be just one “answer” to this question:
the Cournot delocation model might o¤er a compelling rationale for the GATT/WTO e¤orts to
restrict the use of export subsidies in some areas (e.g., agriculture), but not in others (e.g., civil
aircraft). Viewed in this light, and together with existing theories, the Cournot delocation model
and the results we have established here may simply help to provide a more nuanced and complete
understanding of the treatment of export subsidies in trade agreements.
31
Appendix
Proof of Proposition 7: To evaluate (61), we use (59) and …nd that
WPeN
=
WR N
WPe
WR
=
nN
ehN + th @E
h q
th @E
N
= th @E
N
=
Next, using our de…nitions for RN (
N
N
=@ + th @E N =@
N
=@
N
=@
; ) and R
N
(
th @E =@
th @E N =@ :
; ), we see that
N
and
@R
@
N
=
Using (63) and (64), we may now simplify and rewrite (61) as
nN
qhN
h fe
@ PeN
@ Pe
+ qehN
@
@
(63)
nN
ehN
h q
+ th @E N =@
=@
th @E
@ Pe
@RN
=
@
@
N
N
g + th @E
N
@ PeN
@
1:
(64)
=@ + th @E N =@ = 0
(65)
At this point, we exploit the linear-demand structure of the model and calculate the bracketed term in (65).
Using (20) and (23), we …nd that
@ PeN
@ Pe N
qehN
+ qehN
= 0:
@
@
Thus, in the linear Cournot delocation model, the …rst-order condition for the politically optimal domestic
import policy can be rewritten as
th @E N =@ + th @E N =@ = 0:
(66)
We notice that (66) is satis…ed when the domestic country practices free trade with respect to its import
and export policies.
Consider now (62). Using our de…nitions for RN ( ; ) and R N ( ; ), we see that
@RN
@ Pe
=
@
@
@R
@
N
qehN g + th @E
N
N
1 and
=
Using (63) and (67), we may rewrite (62) as
nN
qhN
h fe
@ PeN
@ Pe
+ qehN
@
@
N
@ PeN
:
@
=@
+ th @E N =@
(67)
= 0:
(68)
As above, we now exploit the linear-demand structure of the model and calculate the bracketed term in (68).
Using (21) and (22), we …nd that
qehN
@ PeN
@ Pe
+ qehN
@
@
N
qehN = 0:
Thus, in the linear Cournot delocation model, the …rst-order condition for the politically optimal domestic
export policy can be rewritten as
th @E
N
=@
+ th @E N =@
32
= 0:
(69)
Notice that (69) is also satis…ed when the domestic country practices free trade with respect to its import
and export policies.
We now see that (66) and (69) are satis…ed when th = th = 0. Thus, in the linear Cournot delocation
model, there exists a (symmetric) political optimum in which both countries practice free trade with respect
to their import and export policies. Furthermore, at a symmetric point, we know from (32), (33) and (52),
respectively, that @E N =@ = @E N =@ > 0; @E N =@ = @E N =@ < 0 and @E N =@ + @E N =@ < 0. This
information is su¢ cient to tell us that global free trade is in fact the unique symmetric political optimum.
Proposition 7 is thus established.
33
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34